As usual, the root is self-esteem, and perception is the source of conflict. You do not see what others see. You seem to be giving yourself a low letter grade on a Yes/No or True/False test. "People think of me as having certain skills or abilities, etc..." (True) "...which I don't believe I have to the extent that they seem to think I have..." (Letter Grade = C, maybe D) For example, when someways says, "You did good on that," do you think or is your reply something like, "I could have done better," or "Thank you, but I should have done it quicker."
Also, much of what you originally said is not diamond-cut truth; it is assumptional. Look at how often you use waffle phrases like 'I don't believe, they seem to think, and I feel like. This is clearly a difference of perception, not of fact. Therefore, you can not be a fraud. You do have what others say you have; you just don't see youself as using it well enough. Hence the low grade.
Somewhere in your life, probably early on, your were taught either directly or indirectly that you are either never good enough always or not good enough often. The saving grace here is that you do know you are good.
Damn, I need to stop jabbering so much. One final thought though: You are probably fantastic, wonderful, excellent, stupendous, etc. You just don't see it, which, by the way, reflects the positive quality of humility.

Hoping I didn't say too much, the wrong thing, or at an inappropriate place,
Larry